There are 2 different ways:
1. Use implicite differentiation:
Plug in the coordinates of the tangent point and solve for y':
Therefore the equation of the tangent is
2. is the equation of a circle with the center at the origin and with a radius of 5. The direction from the center to the tangent point is:
The direction of the tangent must be perpendicular to this direction and therefore
Use the point-slope-formula of a straight line to get the equation of the tangent.